The vortex tube, also known as the Ranque-Hilsch vortex tube,
is a mechanical device that separates a compressed gas into hot
and cold streams. It has no moving parts.

Pressurized gas is injected tangentially into a swirl chamber
and accelerates to a high rate of rotation. Due to the conical
nozzle at the end of the tube, only the outer shell of the
compressed gas is allowed to escape at that end. The remainder
of the gas is forced to return in an inner vortex of reduced
diameter within the outer vortex.

There are different explanations for the effect and there is
debate on which explanation is best or correct.

What is usually agreed upon is that the air in the tube
experiences mostly "solid body rotation", which simply means the
rotation rate (angular velocity) of the inner gas is the same as
that of the outer gas. This is different from what most consider
standard vortex behaviour--where inner fluid spins at a higher
rate than outer fluid. The (mostly) solid body rotation is
probably due to the long time which each parcel of air remains
in the vortex--allowing friction between the inner parcels and
outer parcels to have a notable effect.

It is also usually agreed upon that there is a slight effect of
hot air wanting to "rise" toward the center, but this effect is
negligible--especially if turbulence is kept to a minimum.

One simple explanation is that the outer air is under higher
pressure than the inner air (because of centrifugal force).
Therefore the temperature of the outer air is higher than that
of the inner air.

Another explanation is that as both vortices rotate at the same
angular velocity and direction, the inner vortex has lost
angular momentum. The decrease of angular momentum is
transferred as kinetic energy to the outer vortex, resulting in
separated flows of hot and cold gas.[1]

This is somewhat analogous to a Peltier effect device, which
uses electrical pressure (voltage) to move heat to one side of a
dissimilar metal junction, causing the other side to grow cold.

When used to refrigerate, heat-sinking the whole vortex tube is
helpful. Vortex tubes can also be cascaded. The cold (or hot)
output of one can be used to pre-cool (or pre-heat) the air
supply to another vortex tube. Cascaded tubes can be used, for
example, to produce cryogenic temperatures.

History

The vortex tube was invented in 1933 by French physicist
Georges J. Ranque. German physicist Rudolf Hilsch improved the
design and published a widely read paper in 1947 on the device,
which he called a Wirbelrohr (literally, whirl pipe).[2] Vortex
tubes also seem to work with liquids to some extent.[3]

Efficiency

Vortex tubes have lower efficiency than traditional air
conditioning equipment. They are commonly used for inexpensive
spot cooling, when compressed air is available. Commercial
models are designed for industrial applications to produce a
temperature drop of about 45 °C (80 °F).

Proposed applications

* Dave Williams, of dissigno, has proposed using vortex tubes
to make ice in third-world countries. Although the technique is
inefficient, Williams expressed hope that vortex tubes could
yield helpful results in areas where using electricity to create
ice is not an option.

* There are industrial applications that result in unused
pressurized gases. Using vortex tube energy separation may be a
method to recover waste pressure energy from high and low
pressure sources.[4]

Vortex Tubes are an effective, low cost solution to a wide
variety of industrial spot cooling and process cooling needs.
With no moving parts, a vortex tube spins compressed air to
separate the air into cold and hot air streams. While French
physicist Georges Ranque is credited with inventing the vortex
tube in 1930, Vortec was the first company to develop and apply
this phenomenon into practical and effective spot cooling
solutions for industrial use.

Vortex Tube Applications:

Vortex Tubes have a very wide range of application for
industrial spot cooling on machines, assembly lines and
processes.

Fluid (air) that rotates around an axis (like a tornado) is
called a vortex. A Vortex Tube creates cold air and hot air by
forcing compressed air through a generation chamber which spins
the air centrifugally along the inner walls of the Tube at a
high rate of speed (1,000,000 RPM) toward the control valve. A
percentage of the hot, high-speed air is permitted to exit at
the control valve. The remainder of the (now slower) air stream
is forced to counterflow up through the center of the high-speed
air stream, giving up heat, through the center of the generation
chamber finally exiting through the opposite end as extremely
cold air. Vortex tubes generate temperatures down to 100°F below
inlet air temperature. A control valve located in the hot
exhaust end can be used to adjust the temperature drop and rise
for all Vortex Tubes.

Vortex Tubes Features & Benefits

• Vortex Tubes use only compressed air for spot cooling-
no electricity or refrigerants are required

• Vortex Tubes are maintenance free - Since Vortex Tubes have
no moving parts there is no maintence required

Abstract -- Based on the models of Scheper, Lewins, and
Bejan, a new model has been established to study the influence
of the cold mass flow fraction on the temperature separation
effect in a vortex tube. The model is based on making an analogy
between the vortex tube and a counterflow heat exchanger. The
results show the model can accurately explain the correlation of
cold mass flow fraction to the temperature separation effect.

[BILL B. NOTE: also see Scientific American, November 1958 for
a Hilsch-tube construction article in Stong's THE AMATEUR
SCIENTIST]

"It was a Wirbelrohr, he explained; you blew into the stem, and
out one end of the cross-tube flowed hot air, while cold air
flowed out the other. I laughed; I was certain he was teasing
me. Although I had never heard of a Wirbelrohr, I recognised a
Maxwell demon when it was described."

"...he machined in his basement workshop a working model which
I received from him shortly afterwards. The exterior was more or
less just as he had described it: two identical long thin-walled
tubes (the cross-bar of the T), were connected by cylindrical
collars screwed into each end of a short section of pipe that
formed the central chamber; a gas inlet nozzle (the stem of the
T), shorter than the other two tubes but otherwise of identical
construction, joined the midsection tangentially (Fig. 6.1).
Externally, except for a throttling valve at the far end of one
output tube to control air flow, the entire device manifested
bilateral symmetry with respect to a plane through the nozzle
perpendicular to the cross-tubes.

"Only someone with the lung capacity of Hercules could actually
blow into the stem. Instead, the nozzle was meant to be attached
to a source of compressed air. Taking the Wirbelrohr into my
laboratory, I looked sceptically for a moment at its symmetrical
shape before opening the valve by my work table that started the
flow of room-temperature compressed air. Then, with frost
forming on the outside surface of one tube, I yelped with pain
and astonishment when, touching the other tube, I burned my
fingers!"

"...With the few parts of the Wirbelrohr laid out on my table,
I understood better the significance of the German name,
Wirbelrohr, or vortex tube. The heart of the device is the
central chamber with a spiral cavity and offset nozzle.
Compressed gas entering this chamber streams around the walls of
the cavity in a high-speed vortex. But what gives rise to
spatially separated air currents at different temperatures?
...the placement in one cross-tube (the cold one) of a
small-aperture diaphragm effectively blocked the efflux of gas
along the walls of the tube, thereby forcing this part of the
air flow to exit through the other arm whose cross-section was
unconstrained.

Room-temperature compressed air enters the inlet tube, spirals
around the central chamber, and exits through the 'hot' pipe
with unconstrained cross-section or through the 'cold' pipe
whose aperture is restricted by a diaphragm.

[BILLB: the 'hot' tube should be partially blocked, with either
a valve, or even better, a narrow ring-slot that lets air near
the inner surface escape.]

"The glimmer of a potential mechanism dawned on me. Had the in-
coming air conserved angular momentum, the rotational frequency
of air molecules nearest the axis of the central chamber would
be higher - as would also be the corresponding rotational
kinetic energy - than peripheral layers of air. However,
internal friction between gas layers comprising the vortex would
tend to establish a constant angular velocity throughout the
cross-section of the chamber. In other words, each layer of gas
within the vortex would exert a tangential force upon the next
outer layer, thereby doing work upon it at the expense of its
internal energy (while at the same time receiving kinetic energy
from the preceding inner layer). Energy would consequently flow
from the center radially outward to the walls generating a
system with a low-pressure, cooled axial region and a
high-pressure, heated circumferential region. Because of the
diaphragm, the cooler axial air had to exit one tube (the cold
side), whereas a mixture of axial and peripheral air exited the
other (the hot side).

"The presence of the throttling valve on the hot side now made
sense. If the low pressure of the air nearest the axis of the
tube fell below atmospheric pressure, the cold air would not
exit at all...By throttling the flow, pressure within the
central chamber was increased sufficiently so that air could
exit both tubes.

"...with some simplifying assumptions I was able to calculate
the entropy change... Under what is termed adiabatic conditions
- i.e. with no heat exchange with the environment - the 2nd Law
requires that the entropy change of the gas, alone, be >=
zero. The resulting mathematical expression, augmented by the
equation of state of an ideal diatomic gas and the conservation
of energy (1st Law) yields an inequality:

(x^f)[(1-fx)/(1-f)]^(1-f) >= (Pf/Pi)^(2/7)

where x= Tc/Ti
Tc is temperature of cold air
Ti is initial temperature
Pf is the final pressure
Pi is the initial pressure
f is the fraction of gas directed thru the cold side

"By setting the expression for the entropy change equal to
zero, I could calculate the lowest temperature that the cold
tube should be able to reach if the gas flow were an ideal
reversible process. The result was astonishing. With an input
pressure of 10 atmospheres and the throttling set for a fraction
f= 0.3, compressed air at room temperature (20 C) could in
principle be cooled to about -258 C, a mere 15 degrees above
absolute zero! (The corresponding temperature of the hot side
would have been 80 C.)

"...The first experimental demonstation of a vortex tube seems
to have been reported in 1933 by a French engineer, Georges
Ranque [1]. by German physicist Rudolph Hilsch came to the
attention of American chemist R.M. Milton... In Hilsch's hands,
proper selection of the air fraction f (~ .33) and an input
pressure of a few atmospheres gave rise to an amazing output of
200 C at the hot end and -50 C at the cold end[2]. Hilsch, who
was the one to coin the term Wirbelrohr, used the tube in place
of an ammonia pre-cooling apparatus in a machine to liquify air.

"...Milton was not satisfied with the interpretation of Hilsch
and Ranque that frictional loss of kinetic energy produced the
radial temperature distribution...."

"With a loud roar air rushes turbulently thru the Wirbelrohr,
just as it does thru a jet engine or a vacuum cleaner. Buried
within that roar, however, is a pure tone, a "vortex whistle" as
it has been called...the vortex whistle can be produced by
tangential introduction and swirling of gas in a stationary
tube. It is this pure tone that is purportedly responsible for
the spectacular separation of temperature in a vortex tube.

"The Ranque-Hilsch effect is a steady-state phenomenon - i.e.
an effect that survives averaging over time. How can a
high-pitch whistle - a sound that, depending on air velocity and
cavity geometry, can be on the order of a few kilohertz -
influence the steady component of flow? The answer...was by
'acoustic streaming'. As a result of a small nonlinear
convection term in the fluid equation of motion, an acoustic
wave can act back upon the steady flow and modify its properties
substantially. In the absence of unsteady disturbances, the air
flows in a 'free' vortex around the axis of the tube; the speed
of the air is close to zero at the center (like a hurricane),
increases to a maximum at mid-radius, and drops to a small value
near the walls. Acoustic streaming, however, deforms the free
vortex into a 'forced' vortex where the air speed increases
linearly from the center to the periphery. Acoustic streaming
and the production of a forece vortex, rather than mere static
centrifugation, engender the Ranque-Hilsch effect.

"The experimental test could not be more direct. Remove the
whistle, and only the whistle, and see whether the radial
temperature distribution remains. To do this [Kurosaka]
monitored the entireroar with a microphone and ...decomposed it
into frequencies of which the discrete component of the lowest
frequency and largestamplitude was identified as the vortex
whistle. Next, he enclosed the Wirbelrohr inside a tunable
acoustic suppressor: a cylindrical section of Teflon with
radially drilled holes serving as acoustic cavities distributed
uniformly around the circumference. Inside each hole was a small
tuning rod that could be inserted until it touched the outer
shell of the Wirbelrohr to close off the cavity, or withdrawn
incrementally to make the cavity resonant at the specified
frequency to be suppressed.

"To simplify the experimental test, he sealed off one output of
the vortex tube and monitored with thermocouples the temperature
difference between the center and periphery. In the absence of
the suppressor, an increase in pressure produced, as I had
noticed when experimenting with my own vortex tube, a louder
roar and greater temperature difference. When, however, the
acoustic cavity was adjusted to suppress only the frequency of
the vortex whistle (leaving unaffected the rest of the turbulent
noise), the temperature difference plunged precipitously at the
instant the corresponding input air pressure was reached. In one
such trial, the centerline temperature jumped 33 C, from -50 C
to -17 C. With further increase in pressure, the frequency of
the whistle rose, and as it exceeded the narrow band of the
acoustic suppressor, the temperature difference increased again.

"Additional evidence came from a striking transformation in the
nature of the flow...Before the vortex whistle was suppressed,
the exhaust air swirled rapidly near and outside the tube
periphery in the manner expected for a forced vortex. Upon
supprssion, however, the forced vortex was also abruptly
suppressed; now quiescent at the periphery, the air rushed out
close to the centerline."

"For all I know, the case of the mysterious Wirbelrohr is
largely closed although, science being what it is, future
version of that device may yet hold some suprises in store. I
have sometimes wondered, for example, what would result from
supplying a vortex tube, not with room-temperature air, but with
a quantum fluid, like liquid helium, free of viscosity and
friction.

The exorcism of the demon in the Wirbelrohr will not, I
suspect, dampen one bit the ardour of those whose passion it is
to challenge the 2nd Law. Despite the time and effort that has
been frittered away in the past, others will undoubtedly try
again. On the whole such schemes are bound to fail, but every so
often, as in the case of Maxwell's own whimsical creation, this
failure has its positive side: when, from the clash between
human ingenuity and the laws of nature, there emerge sounder
knowledge and deeper understanding."

THE "HILSCH" VORTEX TUBE

With nothing more than a few pieces of plumbing and a source of
compressed air, you can build a remarkably simple device for
attaining moderately low temperatures. It separates high-energy
molecules from those of low energy. George O. Smith, an engineer
of Rumson, N. I., discusses its theory and construction

The 19th century British physicist James Clerk Maxwell made
many deep contributions to physics, and among the most
significant was his law of random distribution. Considering.
the case of a closed box containing a gas, Maxwell started off
by saying that the temperature of the gas was due to the
motion of the individual gas molecules within the box. But
since the box was standing still, it stood to reason that the
summation of the velocity and direction of the individual gas
molecules must come to zero.

In essence Maxwell's law of random distribution says that for
every gas molecule headed east at 20 miles per hour, there
must be another headed west at the same speed. Furthermore, if
the heat of the gas indicates that the average velocity of the
molecules is 20 miles per hour, the number of molecules moving
slower than this speed must be equaled by the number of
molecules moving faster.

After a serious analysis of the consequences of his law,
Maxwell permitted himself a touch of humor. He suggested that
there was a statistical probability that; at some time in the
future, all the molecules in a box of gas or a glass of hot
water might be moving in the same direction. This would cause
the water to rise out of the glass. Next Maxwell suggested
that a system of drawing both hot and cold water out of a
single pipe might be devised if we could capture a small demon
and train him to open and close a tiny valve. The demon would
open the valve only when a fast molecule approached it, and
close the valve against slow molecules. The water coming out
of the valve would thus be hot. To produce a stream of cold
water the demon would open the valve only for slow molecules.

Maxwell's demon would circumvent the law of thermodynamics
which says in essence: "You can't get something for nothing."
That is to say, one cannot separate cold water from hot
without doing work. Thus when physicists heard that the
Germans had developed a device which could achieve low
temperatures by utilizing Maxwell's demon, they were
intrigued, though obviously skeptical. One physicist
investigated the matter at first hand for the U. S. Navy. He
discovered that the device was most ingenious, though not
quite as miraculous as had been rumored.

234

It consists of a T-shaped assembly of pipe joined by a novel
fitting, as depicted in Figure 234. when compressed air is
admitted to the "leg" of the T, hot air comes out of one arm
of the T and cold air out of the other arm! Obviously,
however, work must be done to compress the air.

The origin of the device is obscure. The principle is said to
have been discovered by a Frenchman who left some early
experimental models in the path of the German Army when France
was occupied. These were turned over to a German physicist
named Rudolf Hilsch, who was working on low temperature
refrigerating devices for the German war effort. Hilsch made
some improvements on the Frenchman's design, but found that it
was no more efficient than conventional methods of
refrigeration in achieving fairly low temperatures.
Subsequently the device became known as the Hilsch tube.

235

The Hilsch tube may be constructed from a pair of modified
nuts and associated parts as shown in Figure 235. The
horizontal arm of the T-shaped fitting contains a specially
machined piece, the outside of which fits inside the arm. The
inside of the piece, however, has a cross section which is
spiral with respect to the outside. In the "step" of the
spiral is a small opening which is connected to the leg of the
T Thus air admitted to the leg comes out of the opening and
spins around the one-turn spiral. The "hot" pipe is about 14
inches long and has an inside diameter of half an inch. The
far end of this pipe is fitted with a stopcock which can be
used to control the pressure in the system [see Fig. 236].

236

The "cold" pipe is about four inches long and also has an
inside diameter of half an inch. The end of the pipe which
butts up against the spiral piece is fitted with a washer, the
central hole of which is about a quarter of an inch in
diameter. Washers with larger or smaller holes can also be
inserted to adjust the system.

Three factors determine the performance of the Hilsch tube;
the setting of the stopcock, the pressure at which air is
admitted to the nozzle, and the size of the hole in the
washer. For each value of air pressure and washer opening
there is a setting of the stopcock which results in a maximum
difference in the temperature of the hot and cold pipes [see
Fig. 237].

237

When the device is properly adjusted, the hot pipe will
deliver air at about 100 degrees Fahrenheit and the cold pipe
air at about -70 degrees (a temperature substantially below
the freezing point of mercury and approaching that of "dry
ice"). When the tube is adjusted for maximum temperature on
the hot side, air is delivered at about 350 degrees F. It must
be mentioned, however, that few amateurs have succeeded in
achieving these performance extremes. Most report minimums on
the order of -10 degrees and maximums of about + 140 on the
first try. Despite its impressive performance, the efficiency
of the Hilsch tube leaves much to be desired. Indeed, there is
still disagreement as to how it works. According to one
explanation, the compressed air shoots around the spiral and
forms a high-velocity vortex of air. Molecules of air at the
outside of the vortex are slowed by friction with the wall of
the spiral. Because these slow-moving molecules are subject to
the rules of centrifugal force, they tend to fall toward the
center of the vortex. The fast-moving molecules just inside
the outer layer of the vortex transfer some of their energy to
this layer by bombarding some of its slow-moving molecules and
speeding them up. The net result of this process is the
accumulation of slow-moving, low-energy molecules in the
center of the whirling mass, and of high-energy, fast-moving
molecules around the outside. In the thermodynamics of gases
the terms "high energy" and "high velocity" mean "high
temperature." So the vortex consists of a core of cold air
surrounded by a rim of hot air.

The difference between the temperature of the core and that
of the rim is increased by a secondary effect which takes
advantage of the fact that the temperature of a given quantity
of gas at a given level of thermal energy is higher when the
gas is confined in a small space than in a large one;
accordingly when gas is allowed to expand, its temperature
drops. In the case of the Hilsch tube the action of
centrifugal force compresses the hot rim of gas into a compact
mass which can escape only by flowing along the inner wall of
the "hot" pipe in a compressed state, because its flow into
the cold tube is blocked by the rim of the washer.

The amount of the compression is determined by the adjustment
of the stopcock at the end of the hot pipe. In contrast, the
relatively cold inner core of the vortex, which is also
considerably above atmospheric pressure, flows through the
hole in the washer and drops to still lower temperature as it
expands to atmospheric pressure obtaining inside the cold
pipe.

Apparently the inefficiency of the Hilsch tube as a
refrigerating device has barred its commercial application.
Nonetheless amateurs who would like to have a means of
attaining relatively low temperatures, and who do not have
access to a supply of dry ice, may find the tube useful. when
properly made it will deliver a blast of air 20 times colder
than air which has been chilled by permitting it simply to
expand through a Venturi tube from a high-pressure source.
Thus the Hilsch tube could be used to quick- freeze tissues
for microscopy, or to chill photomultiplier tubes. But quite
apart from the tube's potential application, what could be
more fun than to trap Maxwell's demon and make him explain in
detail how he manages to blow hot and cold at the same time?

Incidentally, this is not a project for the person who goes
in for commercially made apparatus. So far as I can discover
Hilsch tubes are not to be found on the market. You must make
your own. Nor is it a project for the experimenter who makes a
speciality of building apparatus from detailed specifications
and drawings. The dimensions shown in the accompanying figures
are only approximate. Certainly they are not optimum values.
But if you enjoy exploration, the device poses many questions.
What would be the effect, for example, of substituting a
divergent nozzle for the straight one used by Hilsch? Why not
create the vortex by impeller vanes, such as those employed in
the stator of turbines? Would a spiral chamber in the shape of
a torus improve the efficiency? What ratio should the diameter
of the pipes bear to the vortex chamber and to each other? Why
not make the spiral of plastic, or even plastic wood? One can
also imagine a spiral bent of a strip of brass and soldered
into a conventional pipe coupling. Doubtless other and far
more clever alternatives will occur to the dyed-in-the-wool
tinkerer.